How to paint "Noise Texture" with Alpha Transparency? (Image Editor)
Your brush mix mode shouldn't be overlay, the color mix mode of the texture you are painting onto should be overlay. The overlay mix mode of the brush only affects pixels present in the image texture you are painting, causing new pixels to 'overlay' the pixels in the image. Overlay mix mode of the image texture to the next below will affect all the pixels of those underneath in that next image slot, which might be what you are looking for. Another way to do this is to use a Brush Mask texture with color ramp turned on and squeezed for desired contrast, and then pick the color you want to paint through to the image texture.